Question

in the given figure POQ is a triangle with coordinates of P and O as (√13,0) and (0,0) respectively.If PQ=7 units,find the coordinates of Q.

Answer 1

Given:

A triangle Δ POQ is given. Co-ordinate of P and O are  (√13,0) and (0,0) respectively. Length of PQ is 7 units.

To Find:

What is co-ordinate of Q?

Solution:

Here point Q lie on y-axis. So its abscissa will be zero. Let its distance from origin is k along y -axis. So its co-ordinate will be:

Co-ordinate of Q = (0 , k)       ...1)

Means :

OQ = k  unit

Co-ordinate of P = (√13,0)

Means :

OP = √13    unit

PQ = 7    unit             (Given)

We see that in  Δ POQ :

∠QOP = 90°

So  Δ POQ  is a right angle triangle, by Pythagoras' Rule:

OQ² + OP² = PQ²

k² +(√13)² = 7²

k² +13 = 49

k² = 36

So:

k = 6 units

Then Co-ordinate of Q can be obtained by equation 1):

Co-ordinate of Q = (0,6)

Answer 2

Answer:

Coordiante of Q is (0,6)